Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach

TL;DR

This paper introduces DKLM, a data-driven kernel learning approach for nonlinear subspace clustering that adaptively preserves manifold structures and improves robustness over traditional methods.

Contribution

It proposes a novel kernel learning paradigm that directly learns kernels from data, overcoming limitations of predefined kernels and enhancing clustering robustness.

Findings

DKLM effectively preserves local manifold structures.

It produces more accurate affinity matrices for clustering.

Experimental results outperform existing nonlinear clustering methods.

Abstract

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the influence of predefined kernels on model performance; (ii) the difficulty of preserving the original manifold structures in the nonlinear space; (iii) the dependency of spectral-type strategies on the ideal block diagonal structure of the affinity matrix. This paper presents DKLM, a novel paradigm for kernel-induced nonlinear subspace clustering. DKLM provides a data-driven approach that directly learns the kernel from the data's self-representation, ensuring adaptive weighting and satisfying the multiplicative triangle inequality constraint, which enhances the robustness of the learned kernel. By leveraging this learned kernel, DKLM preserves the local manifold structure of data in a nonlinear space while promoting the formation of an optimal block-diagonal affinity matrix. A thorough theoretical examination of DKLM reveals its relationship with existing clustering paradigms. Comprehensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.